Abstract
In this article we examine small sample properties of a generalized method of moments (GMM) estimation using Monte Carlo simulations. We assume that the generated time series describe the stochastic variance rate of a stock index. we use a mean reverting square-root process to simulate the dynamics of this instantaneous variance rate. The time series obtained are used to estimate the parameters of the assumed variance rate process by applying GMM. Our results are described and compared to estimates from empirical data which consist of volatility as well as daily volume data of the German stock market. One of our main findings is that estimates of the mean reverting parameter that are not significantly different from zero do not necessarily imply a rejection of the hypothesis of a mean reverting behavior of the underlying stochastic process.
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This research is part of the program “Effiziente Gestaltung von Finanzmärkten und Finanzinstitionen” supported by the Deutsche Forschungsgemeinschaft. We thank the participants at the 1996 Spring Kolloquium of this program, especially Sigrid Müller and Siegfried Trautmann, for helpful discussions. In particular, we appreciate the suggestions of Robert Jung and Roman Liesenfeld, who also helped us along with the computer programs. The comments of an anonymous referee are gratefully acknowledged. We thank the Deutsche Börse AG for providing us with the data.
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Nagel, H., Schöbel, R. Volatility and GMM — Monte Carlo studies and empirical estimations. Statistical Papers 40, 297–321 (1999). https://doi.org/10.1007/BF02929877
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DOI: https://doi.org/10.1007/BF02929877